Thanks for all the detailed feedback, astoundingly detailed stuff in your posts which I will try to allude to in this post, some of you have similar recommendations
Ok, here goes. I'll slide down the culture until Liberalism and get Espionage running into a full engine. Some of you recommend war (Domination is admittedly a good alternative to culture), but with whom should I war? Caesar? Because then Suleiman would end up hating me and I'll lose the good will I got from cancelling trade with Wang and Pericles. Wang is an easy target now, of course....but Rome is in the way. I *almost* took that city too. My units were just 2 turns late, and I couldn't be stuffed reloading. =|
If you attack someone I would recommend Greece. They are already at war, are hated, their only friend already hates you and their territory is close to yours.
Use

not espionage..... I am pretty certain Gumbolt only meant focusing the esp points you get naturally, putting up the esp slider would be a monumental mistake!
Some more questions:
*Should I change my cultural strategy focus to different cities? I do notice that 2 of the 3 cities I chose are relatively low in pop/prod. compared to say, Cimmercian.
*How do I work the Great People farms? Just spam wonders in high food cities? Or....(yeah I have no idea how GP farms really work)
The most reliable GP farm is one with food that runs specialists. Wonders are just gravy to go on top, not necessary.
*Switch from Vassalage to Bureaucracy? Are there policies that would be better for me later down the tech path?
Vassalage is a poor civic most of the time, and is only worth even considering if your warring a lot. Bureacracy is on the other hand an outstanding civic for the mid game that should be used in almopst all games, its strong enough to build your economy around.
For a culture win Fre Speech will be your ultimate goal in this column, but Burea will help get you there.
Also, Slavery and Caste are both very powerful civics, while Serfdom is more or less worthless, swap out of that too
*Where should I settle more cities? If I knew how to pinpoint locations on an ingame map I would....at this point I'm wondering which parts of the coast I should settle on. The economy is stagnating slightly, though with culture off that should be fixed.
The silver with 2 fish is worth settling, and i'd argue the 4 lakes and horse is too as long as your coastal for the Lighthouse. In the west theres the sheep/copper and clam/horse sites too. Basically, if theres food there better be a damn good reason not to settle it!
*Doesn't cutting down forest lower health? That's why I kept quite a few of them up, actually. =|
A little, but buildings and resource trades are much more effective and chopping gets you hammers to build things earlier. If you end up working unimproved forest tiles as you are in your game you are damaging your economy quite a lot as those tiles a very weak.
*What wonders should I target for my cultural cities, and when should I have my cultural cities pumping out only culture as their production queue? I know this stage has to follow Liberalism and ideally Free Speech, but I'm worried the game might be over by then.
The big one for culture is the Sistine Chapel, it dramatically increases the culture output of your artists and religious buildings. Its so good that many people at higher levels grab it to prevent AIs getting early culture win!
Apart from that you can be opportunistic, Statue of Zeus has a very high culture output for a low cost if you have Ivory, Parthenon or Mausoleum are both very useful, give good culture and give artists GPP as a bonus. Obviously all these have gone, but its food for thought for future games.
You only want to start building culture when your cities have all their culture buildings in place, your cathedrals, theatres and anything else you may be bale to get, especially the cathedrals. Its ages too early to even consider building culture.
Don't worry, you have plenty of time, and the AIs aren't close to even being miles away from any victories yet
*Who should I focus espionage on? Caesar? (Mostly cuz I hate him in nearly all games I play).
Its not too important, but Rome or Greece would be the most obvious choices being your neighbours.